Question

Romeo and Juliet are moving in the xy-plane. Juliet starts at the point (0,20( and moves in a straight line at a constant speed. She will pass through the origin in exactly 5 seconds. Romeo starts at the same time from the point (30,0) and moves in a straight line at a constant speed. He will pass through the origin in exactly 2 seconds. Give the parametric equations for Romeo and Juliet's location t seconds after they start moving.

Juliet
x=10-2t, y=20-4t

Romeo
x=30-15t, y=0

What is need help on is this other question. When will Romeo and Juliet be closest to each other?

Answer 1

Was Juliet at (0,20) (according to the question) or at (10,20) (according to the first parametric equation)?

The distance between them can be calculated by
D(t)=sqrt((x2(t)-x1(t))²+(y2(t)-y1(t))²)
By finding the derivative with respect to t and equating the resulting function to zero, t can be solved.

Hint: they would come within 13.23 units of each other (assuming Juliet was at (10,20) at the start).